The proposed research focuses on the design and analysis of studies of a type which are becoming common in medical research, particularly ophthalmologic research. These studies, either observational or randomized, involve endpoints with two properties: (1) an event, such as progression or onset of disease, which is only detectable by clinical inspection so that its time of occurrence is not known exactly (interval censoring), and (2) patients who begin the study after having been at risk for some time (truncation). For example, the Wisconsin Study of Diabetic Retinopathy examined patients for retinopathy at follow-up times of four and six years (and will do so again in another five years). The time of any observed retinopathy onset is known only with a precision of those intervals. Furthermore, an unknown number of potential subjects were unable to enter the study because of existing retinopathy or related diabetic complications, including death. This contrasts with more traditional trials, in which patients enroll at some uniform baseline such as onset of disease or treatment and are observed for mortality or other event whose timing is precisely determinable. In many ophthalmological trials, it is useful to compute a "survival curve", estimates of the probability of being disease-free at various times (time here may refer to age, duration of disease, or time since treatment). This research will focus on improving existing methods of survival curve calculation for interval censored and truncated data. The goals will be to prove the inadequacy of techniques currently available and to provide superior alternatives. These alternatives will be extended to simultaneously analyze two correlated outcomes (as in results for eyes or other paired organs). Properties of the new methods will be assessed with Monte Carlo experiments. Follow-up studies raise design as well as analysis questions. For example, when should the follow-ups be taken? Too soon and no events are observed. Too late and most individuals will have changed status and, since the timing of those changes is unknown, we will have learned only that the average is less than this long period. The second goal of the research is to formulate methods that resolve this dilemma.